Question

A woman throws her keys straight up at 8.49m/s. Her friend catches them 2.89m higher. How long were the keys in the air

Answer 1

The equation for the path made by a body thrown upward with initial velocity $v$ is

$$h=vt-gt^2/2,$$

express time:

$$t=\frac{v+\sqrt{v^2-2gh}}{g}=1.27\text{ s}.$$